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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 07 Mar 2012 15:31:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/07/t13311523474899lbfgf56gau7.htm/, Retrieved Sun, 28 Apr 2024 19:20:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163701, Retrieved Sun, 28 Apr 2024 19:20:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-03-07 20:31:28] [11011eb66bd10d46e8c3e1885748d37e] [Current]
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Dataseries X:
97,81
97,81
97,34
97,02
96,96
96,89
96,89
96,87
96,63
96,35
96,34
96,39
96,39
96,31
96,28
96,28
96,7
96,66
96,66
96,66
96,72
96,88
96,77
96,74
96,74
96,62
97,04
96,93
96,24
96,21
96,21
96,18
96,2
96,51
96,69
96,77
96,77
96,66
96,75
96,98
96,33
96,37
96,37
96,37
96,44
96,65
97,31
97,41
97,41
97,48
97,29
97,15
97,23
97,15
97,15
97,26
96,99
97,71
97,89
97,81
97,81
97,78
98
98,72
98,85
98,93
98,93
98,95
99,41
99,47
99,57
99,63




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163701&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163701&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163701&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.16208333333330.106287275979824914.145954326435
Geometric Mean97.1579883814389
Harmonic Mean97.1539258088716
Quadratic Mean97.1662108122526
Winsorized Mean ( 1 / 24 )97.16152777777780.105981820665202916.775416462341
Winsorized Mean ( 2 / 24 )97.15902777777780.105071545734759924.693998725822
Winsorized Mean ( 3 / 24 )97.15652777777780.104303930167023931.475234175738
Winsorized Mean ( 4 / 24 )97.13263888888890.09680336640369221003.40145696818
Winsorized Mean ( 5 / 24 )97.13402777777780.09608263342611071010.9426054863
Winsorized Mean ( 6 / 24 )97.13402777777780.09608263342611071010.9426054863
Winsorized Mean ( 7 / 24 )97.12916666666670.09369036966392061036.7038470985
Winsorized Mean ( 8 / 24 )97.11694444444450.08972956214496141082.32941433001
Winsorized Mean ( 9 / 24 )97.02819444444450.06900373263046121406.12965046491
Winsorized Mean ( 10 / 24 )97.01430555555560.06585979630638381473.04290320363
Winsorized Mean ( 11 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 12 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 13 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 14 / 24 )97.00902777777780.06263862864246811548.70931692153
Winsorized Mean ( 15 / 24 )97.00277777777780.06151968978234831576.77612031149
Winsorized Mean ( 16 / 24 )96.99833333333330.05722932480951831694.90612821629
Winsorized Mean ( 17 / 24 )96.96055555555560.04581162050307462116.50569202301
Winsorized Mean ( 18 / 24 )96.97055555555560.03939630953979792461.41216495409
Winsorized Mean ( 19 / 24 )96.97319444444440.03906768853560732482.18407792569
Winsorized Mean ( 20 / 24 )96.95930555555560.03537432646653822740.95128418269
Winsorized Mean ( 21 / 24 )96.95347222222220.03370053595594052876.91187905669
Winsorized Mean ( 22 / 24 )96.94736111111110.03279554023243982956.11416747499
Winsorized Mean ( 23 / 24 )96.93777777777780.03139756067285973087.43022388907
Winsorized Mean ( 24 / 24 )96.92777777777780.02996426028543283234.77959590745
Trimmed Mean ( 1 / 24 )97.14085714285710.102417515739821948.478943676309
Trimmed Mean ( 2 / 24 )97.11897058823530.0980998442544719990.001271931765
Trimmed Mean ( 3 / 24 )97.09712121212120.09344476327375141039.08574231891
Trimmed Mean ( 4 / 24 )97.074843750.08809575873850741101.92414640692
Trimmed Mean ( 5 / 24 )97.0580645161290.08458872996383521147.41129885299
Trimmed Mean ( 6 / 24 )97.03983333333330.08048528365560011205.68418132898
Trimmed Mean ( 7 / 24 )97.02034482758620.07532866703498791287.9604624163
Trimmed Mean ( 8 / 24 )97.00035714285710.06951827017901661395.32178940977
Trimmed Mean ( 9 / 24 )96.98092592592590.06327331842486741532.73019876591
Trimmed Mean ( 10 / 24 )96.97365384615390.06142478069738651578.73829983865
Trimmed Mean ( 11 / 24 )96.96780.05984898682926721620.20787881711
Trimmed Mean ( 12 / 24 )96.96270833333330.05845130389991731658.86305118799
Trimmed Mean ( 13 / 24 )96.95717391304350.05662459055400351712.28035318992
Trimmed Mean ( 14 / 24 )96.95113636363640.05422646108035511787.89348285093
Trimmed Mean ( 15 / 24 )96.94404761904760.05116989025071851894.55258051265
Trimmed Mean ( 16 / 24 )96.9370.04737358346437842046.22477150984
Trimmed Mean ( 17 / 24 )96.92973684210530.04345087126480612230.78925739782
Trimmed Mean ( 18 / 24 )96.92611111111110.04154797910730752332.87185547043
Trimmed Mean ( 19 / 24 )96.92088235294120.04056501053481512389.27294915302
Trimmed Mean ( 20 / 24 )96.91468750.03915947639759642474.87189348499
Trimmed Mean ( 21 / 24 )96.90933333333330.03819771111074142537.04555889167
Trimmed Mean ( 22 / 24 )96.90392857142860.03719439596846342605.3368000274
Trimmed Mean ( 23 / 24 )96.89846153846150.03587453481957292701.03743576891
Trimmed Mean ( 24 / 24 )96.89333333333330.034271225659622827.25030892308
Median96.885
Midrange97.905
Midmean - Weighted Average at Xnp96.9148648648649
Midmean - Weighted Average at X(n+1)p96.9261111111111
Midmean - Empirical Distribution Function96.9148648648649
Midmean - Empirical Distribution Function - Averaging96.9261111111111
Midmean - Empirical Distribution Function - Interpolation96.9261111111111
Midmean - Closest Observation96.9148648648649
Midmean - True Basic - Statistics Graphics Toolkit96.9261111111111
Midmean - MS Excel (old versions)96.9297368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.1620833333333 & 0.106287275979824 & 914.145954326435 \tabularnewline
Geometric Mean & 97.1579883814389 &  &  \tabularnewline
Harmonic Mean & 97.1539258088716 &  &  \tabularnewline
Quadratic Mean & 97.1662108122526 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 97.1615277777778 & 0.105981820665202 & 916.775416462341 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 97.1590277777778 & 0.105071545734759 & 924.693998725822 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 97.1565277777778 & 0.104303930167023 & 931.475234175738 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 97.1326388888889 & 0.0968033664036922 & 1003.40145696818 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 97.1340277777778 & 0.0960826334261107 & 1010.9426054863 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 97.1340277777778 & 0.0960826334261107 & 1010.9426054863 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 97.1291666666667 & 0.0936903696639206 & 1036.7038470985 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 97.1169444444445 & 0.0897295621449614 & 1082.32941433001 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 97.0281944444445 & 0.0690037326304612 & 1406.12965046491 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 97.0143055555556 & 0.0658597963063838 & 1473.04290320363 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 97.0051388888889 & 0.0631845896802816 & 1535.2657883788 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 97.0051388888889 & 0.0631845896802816 & 1535.2657883788 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 97.0051388888889 & 0.0631845896802816 & 1535.2657883788 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 97.0090277777778 & 0.0626386286424681 & 1548.70931692153 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 97.0027777777778 & 0.0615196897823483 & 1576.77612031149 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 96.9983333333333 & 0.0572293248095183 & 1694.90612821629 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 96.9605555555556 & 0.0458116205030746 & 2116.50569202301 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 96.9705555555556 & 0.0393963095397979 & 2461.41216495409 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 96.9731944444444 & 0.0390676885356073 & 2482.18407792569 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 96.9593055555556 & 0.0353743264665382 & 2740.95128418269 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 96.9534722222222 & 0.0337005359559405 & 2876.91187905669 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 96.9473611111111 & 0.0327955402324398 & 2956.11416747499 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 96.9377777777778 & 0.0313975606728597 & 3087.43022388907 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 96.9277777777778 & 0.0299642602854328 & 3234.77959590745 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 97.1408571428571 & 0.102417515739821 & 948.478943676309 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 97.1189705882353 & 0.0980998442544719 & 990.001271931765 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 97.0971212121212 & 0.0934447632737514 & 1039.08574231891 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 97.07484375 & 0.0880957587385074 & 1101.92414640692 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 97.058064516129 & 0.0845887299638352 & 1147.41129885299 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 97.0398333333333 & 0.0804852836556001 & 1205.68418132898 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 97.0203448275862 & 0.0753286670349879 & 1287.9604624163 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 97.0003571428571 & 0.0695182701790166 & 1395.32178940977 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 96.9809259259259 & 0.0632733184248674 & 1532.73019876591 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 96.9736538461539 & 0.0614247806973865 & 1578.73829983865 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 96.9678 & 0.0598489868292672 & 1620.20787881711 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 96.9627083333333 & 0.0584513038999173 & 1658.86305118799 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 96.9571739130435 & 0.0566245905540035 & 1712.28035318992 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 96.9511363636364 & 0.0542264610803551 & 1787.89348285093 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 96.9440476190476 & 0.0511698902507185 & 1894.55258051265 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 96.937 & 0.0473735834643784 & 2046.22477150984 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 96.9297368421053 & 0.0434508712648061 & 2230.78925739782 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 96.9261111111111 & 0.0415479791073075 & 2332.87185547043 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 96.9208823529412 & 0.0405650105348151 & 2389.27294915302 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 96.9146875 & 0.0391594763975964 & 2474.87189348499 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 96.9093333333333 & 0.0381977111107414 & 2537.04555889167 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 96.9039285714286 & 0.0371943959684634 & 2605.3368000274 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 96.8984615384615 & 0.0358745348195729 & 2701.03743576891 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 96.8933333333333 & 0.03427122565962 & 2827.25030892308 \tabularnewline
Median & 96.885 &  &  \tabularnewline
Midrange & 97.905 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.9148648648649 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.9261111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.9148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.9261111111111 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.9261111111111 &  &  \tabularnewline
Midmean - Closest Observation & 96.9148648648649 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.9261111111111 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.9297368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163701&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]97.1620833333333[/C][C]0.106287275979824[/C][C]914.145954326435[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]97.1579883814389[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]97.1539258088716[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]97.1662108122526[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]97.1615277777778[/C][C]0.105981820665202[/C][C]916.775416462341[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]97.1590277777778[/C][C]0.105071545734759[/C][C]924.693998725822[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]97.1565277777778[/C][C]0.104303930167023[/C][C]931.475234175738[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]97.1326388888889[/C][C]0.0968033664036922[/C][C]1003.40145696818[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]97.1340277777778[/C][C]0.0960826334261107[/C][C]1010.9426054863[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]97.1340277777778[/C][C]0.0960826334261107[/C][C]1010.9426054863[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]97.1291666666667[/C][C]0.0936903696639206[/C][C]1036.7038470985[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]97.1169444444445[/C][C]0.0897295621449614[/C][C]1082.32941433001[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]97.0281944444445[/C][C]0.0690037326304612[/C][C]1406.12965046491[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]97.0143055555556[/C][C]0.0658597963063838[/C][C]1473.04290320363[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]97.0051388888889[/C][C]0.0631845896802816[/C][C]1535.2657883788[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]97.0051388888889[/C][C]0.0631845896802816[/C][C]1535.2657883788[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]97.0051388888889[/C][C]0.0631845896802816[/C][C]1535.2657883788[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]97.0090277777778[/C][C]0.0626386286424681[/C][C]1548.70931692153[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]97.0027777777778[/C][C]0.0615196897823483[/C][C]1576.77612031149[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]96.9983333333333[/C][C]0.0572293248095183[/C][C]1694.90612821629[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]96.9605555555556[/C][C]0.0458116205030746[/C][C]2116.50569202301[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]96.9705555555556[/C][C]0.0393963095397979[/C][C]2461.41216495409[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]96.9731944444444[/C][C]0.0390676885356073[/C][C]2482.18407792569[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]96.9593055555556[/C][C]0.0353743264665382[/C][C]2740.95128418269[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]96.9534722222222[/C][C]0.0337005359559405[/C][C]2876.91187905669[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]96.9473611111111[/C][C]0.0327955402324398[/C][C]2956.11416747499[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]96.9377777777778[/C][C]0.0313975606728597[/C][C]3087.43022388907[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]96.9277777777778[/C][C]0.0299642602854328[/C][C]3234.77959590745[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]97.1408571428571[/C][C]0.102417515739821[/C][C]948.478943676309[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]97.1189705882353[/C][C]0.0980998442544719[/C][C]990.001271931765[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]97.0971212121212[/C][C]0.0934447632737514[/C][C]1039.08574231891[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]97.07484375[/C][C]0.0880957587385074[/C][C]1101.92414640692[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]97.058064516129[/C][C]0.0845887299638352[/C][C]1147.41129885299[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]97.0398333333333[/C][C]0.0804852836556001[/C][C]1205.68418132898[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]97.0203448275862[/C][C]0.0753286670349879[/C][C]1287.9604624163[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]97.0003571428571[/C][C]0.0695182701790166[/C][C]1395.32178940977[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]96.9809259259259[/C][C]0.0632733184248674[/C][C]1532.73019876591[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]96.9736538461539[/C][C]0.0614247806973865[/C][C]1578.73829983865[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]96.9678[/C][C]0.0598489868292672[/C][C]1620.20787881711[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]96.9627083333333[/C][C]0.0584513038999173[/C][C]1658.86305118799[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]96.9571739130435[/C][C]0.0566245905540035[/C][C]1712.28035318992[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]96.9511363636364[/C][C]0.0542264610803551[/C][C]1787.89348285093[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]96.9440476190476[/C][C]0.0511698902507185[/C][C]1894.55258051265[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]96.937[/C][C]0.0473735834643784[/C][C]2046.22477150984[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]96.9297368421053[/C][C]0.0434508712648061[/C][C]2230.78925739782[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]96.9261111111111[/C][C]0.0415479791073075[/C][C]2332.87185547043[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]96.9208823529412[/C][C]0.0405650105348151[/C][C]2389.27294915302[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]96.9146875[/C][C]0.0391594763975964[/C][C]2474.87189348499[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]96.9093333333333[/C][C]0.0381977111107414[/C][C]2537.04555889167[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]96.9039285714286[/C][C]0.0371943959684634[/C][C]2605.3368000274[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]96.8984615384615[/C][C]0.0358745348195729[/C][C]2701.03743576891[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]96.8933333333333[/C][C]0.03427122565962[/C][C]2827.25030892308[/C][/ROW]
[ROW][C]Median[/C][C]96.885[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.905[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.9148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.9261111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.9148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.9261111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.9261111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.9148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.9261111111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.9297368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163701&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163701&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean97.16208333333330.106287275979824914.145954326435
Geometric Mean97.1579883814389
Harmonic Mean97.1539258088716
Quadratic Mean97.1662108122526
Winsorized Mean ( 1 / 24 )97.16152777777780.105981820665202916.775416462341
Winsorized Mean ( 2 / 24 )97.15902777777780.105071545734759924.693998725822
Winsorized Mean ( 3 / 24 )97.15652777777780.104303930167023931.475234175738
Winsorized Mean ( 4 / 24 )97.13263888888890.09680336640369221003.40145696818
Winsorized Mean ( 5 / 24 )97.13402777777780.09608263342611071010.9426054863
Winsorized Mean ( 6 / 24 )97.13402777777780.09608263342611071010.9426054863
Winsorized Mean ( 7 / 24 )97.12916666666670.09369036966392061036.7038470985
Winsorized Mean ( 8 / 24 )97.11694444444450.08972956214496141082.32941433001
Winsorized Mean ( 9 / 24 )97.02819444444450.06900373263046121406.12965046491
Winsorized Mean ( 10 / 24 )97.01430555555560.06585979630638381473.04290320363
Winsorized Mean ( 11 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 12 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 13 / 24 )97.00513888888890.06318458968028161535.2657883788
Winsorized Mean ( 14 / 24 )97.00902777777780.06263862864246811548.70931692153
Winsorized Mean ( 15 / 24 )97.00277777777780.06151968978234831576.77612031149
Winsorized Mean ( 16 / 24 )96.99833333333330.05722932480951831694.90612821629
Winsorized Mean ( 17 / 24 )96.96055555555560.04581162050307462116.50569202301
Winsorized Mean ( 18 / 24 )96.97055555555560.03939630953979792461.41216495409
Winsorized Mean ( 19 / 24 )96.97319444444440.03906768853560732482.18407792569
Winsorized Mean ( 20 / 24 )96.95930555555560.03537432646653822740.95128418269
Winsorized Mean ( 21 / 24 )96.95347222222220.03370053595594052876.91187905669
Winsorized Mean ( 22 / 24 )96.94736111111110.03279554023243982956.11416747499
Winsorized Mean ( 23 / 24 )96.93777777777780.03139756067285973087.43022388907
Winsorized Mean ( 24 / 24 )96.92777777777780.02996426028543283234.77959590745
Trimmed Mean ( 1 / 24 )97.14085714285710.102417515739821948.478943676309
Trimmed Mean ( 2 / 24 )97.11897058823530.0980998442544719990.001271931765
Trimmed Mean ( 3 / 24 )97.09712121212120.09344476327375141039.08574231891
Trimmed Mean ( 4 / 24 )97.074843750.08809575873850741101.92414640692
Trimmed Mean ( 5 / 24 )97.0580645161290.08458872996383521147.41129885299
Trimmed Mean ( 6 / 24 )97.03983333333330.08048528365560011205.68418132898
Trimmed Mean ( 7 / 24 )97.02034482758620.07532866703498791287.9604624163
Trimmed Mean ( 8 / 24 )97.00035714285710.06951827017901661395.32178940977
Trimmed Mean ( 9 / 24 )96.98092592592590.06327331842486741532.73019876591
Trimmed Mean ( 10 / 24 )96.97365384615390.06142478069738651578.73829983865
Trimmed Mean ( 11 / 24 )96.96780.05984898682926721620.20787881711
Trimmed Mean ( 12 / 24 )96.96270833333330.05845130389991731658.86305118799
Trimmed Mean ( 13 / 24 )96.95717391304350.05662459055400351712.28035318992
Trimmed Mean ( 14 / 24 )96.95113636363640.05422646108035511787.89348285093
Trimmed Mean ( 15 / 24 )96.94404761904760.05116989025071851894.55258051265
Trimmed Mean ( 16 / 24 )96.9370.04737358346437842046.22477150984
Trimmed Mean ( 17 / 24 )96.92973684210530.04345087126480612230.78925739782
Trimmed Mean ( 18 / 24 )96.92611111111110.04154797910730752332.87185547043
Trimmed Mean ( 19 / 24 )96.92088235294120.04056501053481512389.27294915302
Trimmed Mean ( 20 / 24 )96.91468750.03915947639759642474.87189348499
Trimmed Mean ( 21 / 24 )96.90933333333330.03819771111074142537.04555889167
Trimmed Mean ( 22 / 24 )96.90392857142860.03719439596846342605.3368000274
Trimmed Mean ( 23 / 24 )96.89846153846150.03587453481957292701.03743576891
Trimmed Mean ( 24 / 24 )96.89333333333330.034271225659622827.25030892308
Median96.885
Midrange97.905
Midmean - Weighted Average at Xnp96.9148648648649
Midmean - Weighted Average at X(n+1)p96.9261111111111
Midmean - Empirical Distribution Function96.9148648648649
Midmean - Empirical Distribution Function - Averaging96.9261111111111
Midmean - Empirical Distribution Function - Interpolation96.9261111111111
Midmean - Closest Observation96.9148648648649
Midmean - True Basic - Statistics Graphics Toolkit96.9261111111111
Midmean - MS Excel (old versions)96.9297368421053
Number of observations72



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')